The database currently contains 562,396,733 Galois orbits of 303,963,552,392 Dirichlet characters of modulus up to 1,000,000. The tables below count Galois orbits.
Distribution of conductors
| conductor | 1-10 | 11-100 | 101-1000 | 1001-10000 | 10001-100000 | 100001-1000000 |
|---|---|---|---|---|---|---|
| count | 2884126 | 7364817 | 20490247 | 56586458 | 147913142 | 327157943 |
| proportion | 0.51% | 1.31% | 3.64% | 10.06% | 26.30% | 58.17% |
Distribution of order by modulus
| modulus | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1-10 | 11-100 | 101-1000 | 1001-10000 | 10001-100000 | 100001-1000000 | Total | ||
|
order
|
1-10 | 26 | 695 | 13681 | 236212 | 3684354 | 53948867 | 57883835 |
| 100.00% | 80.25% | 52.70% | 31.85% | 18.17% | 9.97% | 10.29% | ||
| 11-100 | 171 | 10719 | 362601 | 9424419 | 211283340 | 221081250 | ||
| 19.75% | 41.29% | 48.89% | 46.48% | 39.03% | 39.31% | |||
| 101-1000 | 1560 | 129250 | 5692433 | 189906572 | 195729815 | |||
| 6.01% | 17.43% | 28.07% | 35.08% | 34.80% | ||||
| 1001-10000 | 13597 | 1356507 | 71608068 | 72978172 | ||||
| 1.83% | 6.69% | 13.23% | 12.98% | |||||
| 10001-100000 | 119107 | 13536170 | 13655277 | |||||
| 0.59% | 2.50% | 2.43% | ||||||
| 100001-1000000 | 1068384 | 1068384 | ||||||
| 0.20% | 0.19% | |||||||
| Total | 26 | 866 | 25960 | 741660 | 20276820 | 541351401 | 562396733 | |
| 0.00% | 0.00% | 0.00% | 0.13% | 3.61% | 96.26% | |||
Distribution of primitivity by modulus
| modulus | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1-10 | 11-100 | 101-1000 | 1001-10000 | 10001-100000 | 100001-1000000 | Total | ||
|
primitive
|
no | 14 | 517 | 16485 | 480433 | 13321362 | 358599884 | 372418695 |
| 53.85% | 59.70% | 63.50% | 64.78% | 65.70% | 66.24% | 66.22% | ||
| yes | 12 | 349 | 9475 | 261227 | 6955458 | 182751517 | 189978038 | |
| 46.15% | 40.30% | 36.50% | 35.22% | 34.30% | 33.76% | 33.78% | ||
| Total | 26 | 866 | 25960 | 741660 | 20276820 | 541351401 | 562396733 | |
| 0.00% | 0.00% | 0.00% | 0.13% | 3.61% | 96.26% | |||
Distribution of real characters by modulus
| modulus | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1-10 | 11-100 | 101-1000 | 1001-10000 | 10001-100000 | 100001-1000000 | Total | ||
|
real
|
no | 6 | 548 | 21522 | 684672 | 19581080 | 533133915 | 553421743 |
| 23.08% | 63.28% | 82.90% | 92.32% | 96.57% | 98.48% | 98.40% | ||
| yes | 20 | 318 | 4438 | 56988 | 695740 | 8217486 | 8974990 | |
| 76.92% | 36.72% | 17.10% | 7.68% | 3.43% | 1.52% | 1.60% | ||
| Total | 26 | 866 | 25960 | 741660 | 20276820 | 541351401 | 562396733 | |
| 0.00% | 0.00% | 0.00% | 0.13% | 3.61% | 96.26% | |||
Distribution of minimality by modulus
| modulus | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1-10 | 11-100 | 101-1000 | 1001-10000 | 10001-100000 | 100001-1000000 | Total | ||
|
minimal
|
no | 1 | 71 | 2807 | 90797 | 2733617 | 78135968 | 80963261 |
| 3.85% | 8.20% | 10.81% | 12.24% | 13.48% | 14.43% | 14.40% | ||
| yes | 25 | 795 | 23153 | 650863 | 17543203 | 463215433 | 481433472 | |
| 96.15% | 91.80% | 89.19% | 87.76% | 86.52% | 85.57% | 85.60% | ||
| Total | 26 | 866 | 25960 | 741660 | 20276820 | 541351401 | 562396733 | |
| 0.00% | 0.00% | 0.00% | 0.13% | 3.61% | 96.26% | |||